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Pertanyaan

Tentukan HP dari pertidaksamaan begin mathsize 14px style log presuperscript 4 space open parentheses 2 x squared plus 24 close parentheses less or equal than log presuperscript 4 space open parentheses x squared plus 10 x close parentheses end style.

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

himpunan penyelesaian dari pertidaksamaan begin mathsize 14px style log presuperscript 4 space open parentheses 2 x squared plus 24 close parentheses less or equal than log presuperscript 4 space open parentheses x squared plus 10 x close parentheses end style adalah begin mathsize 14px style open curly brackets x vertical line 4 less or equal than x less or equal than 6 close curly brackets end style.

Pembahasan

Gunakan sifat.

begin mathsize 14px style Untuk space a greater than 1 space berlaku colon space log presuperscript a space f open parentheses x close parentheses less or equal than log presuperscript a space g open parentheses x close parentheses rightwards arrow f open parentheses x close parentheses less or equal than g open parentheses x close parentheses end style 

Perhatikan perhitungan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell log presuperscript 4 space open parentheses 2 x squared plus 24 close parentheses end cell less or equal than cell log presuperscript 4 space open parentheses x squared plus 10 x close parentheses end cell row cell 2 x squared plus 24 end cell less or equal than cell x squared plus 10 x end cell row cell 2 x squared plus 24 minus x squared minus 10 x end cell less or equal than 0 row cell x squared minus 10 x plus 24 end cell less or equal than 0 row cell open parentheses x minus 4 close parentheses open parentheses x minus 6 close parentheses end cell less or equal than 0 row cell 4 less or equal than x less or equal than 6 end cell blank blank end table end style 

 

Jadi, himpunan penyelesaian dari pertidaksamaan begin mathsize 14px style log presuperscript 4 space open parentheses 2 x squared plus 24 close parentheses less or equal than log presuperscript 4 space open parentheses x squared plus 10 x close parentheses end style adalah begin mathsize 14px style open curly brackets x vertical line 4 less or equal than x less or equal than 6 close curly brackets end style.

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